(2x-6)(3-6x)=0

Solution for (2x-6)(3-6x)=0 equation:

(2x-6)(3-6x)=0

We add all the numbers together, and all the variables

(2x-6)(-6x+3)=0

We multiply parentheses ..

(-12x^2+6x+36x-18)=0

We get rid of parentheses

-12x^2+6x+36x-18=0

We add all the numbers together, and all the variables

-12x^2+42x-18=0

a = -12; b = 42; c = -18;
Δ = b2-4ac
Δ = 422-4·(-12)·(-18)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30}{2*-12}=\frac{-72}{-24}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30}{2*-12}=\frac{-12}{-24}
=1/2
$